They were taken using a one second exposure without a tripod, the camera
was stabilised by jamming it against the sides of a palm tree. This means that
they don't stitch easily because of the large (approximately 60cm) parallax
error:

Particularly, the nadir doesn't work at all. This is an extreme version of the
usual problems caused by failing to rotate the camera around the No-parallax point:

However the nadir can be stitched by taking advantage of another technique generally
used for stitching a linear panorama. The way this works is that if you assume
the ground forms a plane just like a mural on a wall; a series of
rectilinear Projection images taken from different locations can be assembled by
optimising roll, pitch & yaw, Field of View and d & e lens
correction parameters separately for each image.

These can then be stitched together into a single nadir image with minimal errors,
in this case I chose a fisheye projection, though a rectilinear or equirectangular
projection would work just as well:

This image can then be reinserted into the original panorama project as another
source photo with a different lens and stitched as normal. Here is the result as a
QTVR, the buildings in the distance are a bit wobbly, but this could have been
corrected with vertical control points:

This scene is of the Abu Dhabi corniche, 30th November 2006. The buildings are decorated
in preparation for UAE national day.